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April 20, 2014

April 20, 2014

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**Physics**

110 km/hr(1000/3600) = 30.6 m/s 119 km/hr = 33.1 m/s x position of truck = -211.7+ 30.6 t v car = 2.3 t until v = 33.1 at t = 14.4 s and x = (1/2)(2.3)(14.4^2) = 238 m after that xcar = 238 + 33.1 (t-14.4) so during car acceleration period: d = Xcar - Xtruck = .5(2.3)t^2 - 211...
*Sunday, March 2, 2014 at 3:47pm*

**Calculus Please help!**

the linearization is just finding a straight line that is close to the curve at the given point. That is just the tangent line. So, since when y = √(1+2x), y' = 1/√(1+2x) y(0) = 1 y'(0) = 1 and the point-slope form for the line is y-1 = 1(x-0) y = x+1 A=1 ...
*Saturday, March 1, 2014 at 6:28am*

**Pre-Calculus**

Reiny gave you good polar coordinates, but if all you want is parametric equations, try x = t/3 y = 1 + t/2 or x = -(2+t)/3 y = -2t
*Saturday, March 1, 2014 at 6:20am*

**Pre-Calculus**

y = v sinθ t - 16t^2 x = v cosθ t You have θ and v, so plug those in and solve for x when y=10 to get the max goal distance. or, y = x tanθ - 16/(v cosθ)^2 x^2
*Saturday, March 1, 2014 at 6:15am*

**Pre-Calculus**

we know x =rcosØ and y = rsinØ -3rcosØ + (1/2)rsinØ = 2 -6rcosØ + rsinØ = 2 r(sinØ - 6cosØ) = 2 or r = 2/(sinØ - 6cosØ) looks good: http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx+-+6cosx%29
*Friday, February 28, 2014 at 9:19pm*

**Pre-Calculus**

Phil Dawson is a professional place kicker for the Cleveland Browns. On average, he kicks the ball at a 41 degree angle with an initial speed of 70 feet per second. For future reference, goal posts are 10 feet high in the NFL. a) Write parametric equations to model Dawson'...
*Friday, February 28, 2014 at 8:56pm*

**Pre-Calculus**

Write Parametric equations of -3x+1/2y=2
*Friday, February 28, 2014 at 8:49pm*

**Pre-Calculus**

Jake serves a volleyball with an initial velocity of 32 feet per second from 4.5 feet above the ground at an angle 0f 35 degrees. a) Write parametric equations to model the situation. b) How far will the ball travel( if it hits the ground)show work
*Friday, February 28, 2014 at 8:47pm*

**Calculus Please help!**

dy/dx = 3(x^2 + 6)^2 dy = 3(x^2 + 6)^2 dx when x = 2 and dx = .05 dy = ...... just plug in the above values.
*Friday, February 28, 2014 at 8:41pm*

**Calculus Please help!**

The linearization at a=0 to sqrt(1+2x) is A+Bx where A is____ and where B is _____? A=? B=? Ty
*Friday, February 28, 2014 at 8:20pm*

**Calculus Please help!**

The differential of the function y=(x^2+6)^3 is dy=______dx. When x=2 and dx=0.05, the differential dy=_______? A) dy=______dx? B) the differential dy=_______?
*Friday, February 28, 2014 at 8:19pm*

**Calculus Please help!**

darn them brackets 23t^2 vs (23t)^2
*Friday, February 28, 2014 at 5:26pm*

**Calculus Please help!**

let the time be t hours past noon. I see a right-angled triangle , with sides 23t and 50 + 18t, with D as the distance between them D^2 = (23t)^2 + (50+18t)^2 D^2 = 529t^2 + 2500 + 1800t + 324t^2 = 853t^2 + 1800t + 2500 2D dD/dt = 1706t + 1800 dD/t = (853t + 900)/D , #1 at 3:...
*Friday, February 28, 2014 at 5:23pm*

**Calculus Please help!**

so, did you draw a diagram as suggested? a = 1/2 bh so, b = 2a/h da/dt = 1/2 (db/dt * h + b * dh/dt) Now just plug in your values: 3500 = 1/2 (db/dt * 7000 + 2*87/7 * 2500) db/dt = -7.88
*Friday, February 28, 2014 at 4:55pm*

**Calculus Please help!**

As usual, draw a diagram. The distance between the ships at time t hours is d^2 = (50+18t)^2 + 23t^2 At 3 pm, t=3, so d = √(104^2+69^2) = 124.8 2d dd/dt = 36(50+18t)+46t so, dd/dt = 15.6 knots
*Friday, February 28, 2014 at 4:45pm*

**Calculus Please help!**

Let the radius be r, so the diameter is 2r then the height is 2r V = (1/3)π r^2 h = (1/3) π r^2 (2r) = (2/3)π r^3 dV/dt = 2π r^2 dr/dt when h = 24 2r = 24 r = 12 and dV/dt = 30 30 = 2π (144) dr/dt dr/dt = 30/(288π) = 5/(48π) ft/min or appr ....
*Friday, February 28, 2014 at 4:00pm*

**Calculus Please help!**

Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 24 feet high? Recall that...
*Friday, February 28, 2014 at 3:10pm*

**Calculus Please help!**

At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 23 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)
*Friday, February 28, 2014 at 3:02pm*

**Calculus Please help!**

The altitude of a triangle is increasing at a rate of 2500 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7000 centimeters and the area is 87000...
*Friday, February 28, 2014 at 2:51pm*

**Calculus Help**

f(x) = 1/[ x^.5 +1 ] f(z) = 1/[ z^.5 + 1 } f(x)-f(z) = 1/[ x^.5 +1 ] - 1/[ z^.5 + 1] = ([z^.5+1]-[x^.5+1])/(x^.5z^.5 +x^.5+z^.5+1) = (z^.5-x^.5) /(x^.5z^.5 +x^.5+z^.5+1) Divide by (x-z) which is (x^.5-z^.5)(x^.5+z^.5) and get -(x^.5+z^.5) / (x^.5z^.5 +x^.5+z^.5+1) let z --->...
*Friday, February 28, 2014 at 1:10pm*

**Calculus Help**

Use f(x)= 1/(square root(x)+1) to answer the following; -- Use the difference quotient f'(x)=lim z->x (f(x)-f(z))/ (x-z) to find f'(x)! Please show steps!!! Thank you!!!
*Friday, February 28, 2014 at 12:31pm*

**calculus**

I think we went through this before. note I think the somewhat unusual exponent notation may mean | x^2 + x^-2| = | x^2 + 1/x^2 | http://www.wolframalpha.com/input/?i=plot+y%3D|+x^2+%2B+1%2Fx^2+|
*Friday, February 28, 2014 at 9:53am*

**calculus**

the graph can be seen here: http://www.wolframalpha.com/input/?i=plot+y%3D|x^2+%2Bx-2|+for+-4+%3C%3D+x+%3C%3D+3 That should make it easy to answer the other questions. If not, come on back and show where you get stuck.
*Friday, February 28, 2014 at 6:40am*

**calculus **

Find the asymptote, interval of monotonicity, critical points, the local extreme points, intervals of concavity and inflection point of the following functions. Sketch the graph. a)f(x)=|x2 +x-2|
*Friday, February 28, 2014 at 3:32am*

**Calculus**

by the time you get to calculus, you certainly should know how to plug in a value and evaluate a function! Where do you get stuck? (a) q(5) = 10300*e^(-0.34*5) = 1882 (b) as you know, if y = e^u y' = e^u u' And, as you know, the derivative is the rate of change. So, q...
*Thursday, February 27, 2014 at 11:33pm*

**Calculus**

q = f(p) = 10300e^−0.34p a) Find the number of products sold when the price of the product is $5. (Round your answer to the nearest whole number.) Number of products sold: b) Find a formula for the rate of change in the number of products sold when the price is p dollars...
*Thursday, February 27, 2014 at 10:11pm*

**Calculus Help**

get a better table
*Thursday, February 27, 2014 at 6:18pm*

**Calculus Help**

Let P(t) be the percentage of Americans under the age of 18 at time t. The table gives values of this function in census years from 1950 to 2000. How would it be possible to get more accurate values for P'(t).
*Thursday, February 27, 2014 at 5:06pm*

**calculus**

given the student's use of strange exponent notation it might be |x^2 + 1/x^2 | http://www.wolframalpha.com/input/?i=|x^2+%2Bx^-2|
*Thursday, February 27, 2014 at 3:20pm*

**calculus**

Or, post your results and we can verify them.
*Thursday, February 27, 2014 at 2:50pm*

**calculus**

assuming you just need to confirm your answers, I'll say none |x+.5|>1.5 monotone over any interval not including the x-values -2,-.5,1 up: x<-2 and x>1 down: -2<x<1 no inflection http://www.wolframalpha.com/input/?i=|x^2+%2Bx-2|
*Thursday, February 27, 2014 at 2:49pm*

**calculus**

Find the asymptote, interval of monotonicity, critical points, the local extreme points, intervals of concavity and inflection point of the following functions. Sketch the graph. f(x)= x^2-6x/(x+1)^2
*Thursday, February 27, 2014 at 2:47pm*

**calculus **

Find the asymptote, interval of monotonicity, critical points, the local extreme points, intervals of concavity and inflection point of the following functions. Sketch the graph. a)f(x)=|x2 +x-2|
*Thursday, February 27, 2014 at 2:43pm*

**calculus I**

T = angle up from center of sphere to intersection of cylinder and sphere r = 10 height of cylinder = 2 r sin T radius of cylinder = r cos T volume of cylinder = V = pi(r^2 cos^2 T)(2 r sin T) = 2pi r^2 (cos^2 T sin T) dV/dT = 0 for max = cos^3 T - 2 sin^2T cos T = cosT ( cos^...
*Thursday, February 27, 2014 at 12:27pm*

**calculus I**

Find the dimension of the right circular cylinder of the largest volume that can inscribed in a Sphere of radius 10 units.
*Thursday, February 27, 2014 at 11:48am*

**Business Math**

A local Barnes and Noble paid a $79.33 net price for each calculus textbook. The publisher offered a 10% trade discount. What was the publisher’s list price? (Round your answer to the nearest cent.)
*Thursday, February 27, 2014 at 1:14am*

**math- calculus**

You will often see proj (Vector a onto Vector b) written as projb⃗ a⃗ .Show that projb⃗ a⃗ =(a⃗ ⋅b⃗/ b⃗ ⋅b⃗ )*b⃗ .
*Wednesday, February 26, 2014 at 8:11pm*

**ap calculus.linear**

thank u so much steve. i have trouble with word problems. now i understand.
*Wednesday, February 26, 2014 at 12:19pm*

**ap calculus.linear**

earnings = 0.05 A•f A+f is meaningless, since you can't add ft^2 and n. A•f computes the total ft^2 mowed. For various earnings, you'd also need a vector of rates. Not sure how to do that with just vector operations. Say the rates were 0.05, 0.10, 0.07, 0.12...
*Wednesday, February 26, 2014 at 6:36am*

**ap calculus.linear**

i dont clearly understand questions 1 and 2. so the question have to be A+f??? When he was young, Captain Conundrum mowed lawns on weekends to help pay his college tuition bills. He charged his customers according to the size of their lawns at a rate of 5¢ per square foot...
*Wednesday, February 26, 2014 at 3:11am*

**Calculus**

1
*Tuesday, February 25, 2014 at 10:15pm*

**Calculus Help Please!!!**

f(x+h) = (x + h) + 1/(x+h) = [(x+h)^2 + 1] /(x+h) = [x^2 + 2 x h + h^2 + 1 ] / (x+h) f(x) = (x^2+1)/x f(x+h) - f(x) =[x^2+2xh+h^2+1]/(x+h) - (x^2+1)/x = x^3+2x^2h+h^2x+x -(x^2+1)(x+h) -------------------------------- x^2 + hx divide by h x^3+2x^2h+h^2x+x -(x^2+1)(x+h...
*Tuesday, February 25, 2014 at 7:44pm*

**Calculus Help Please!!! **

if f(x)= x+(1/x), find f'(x) using the limit definition of derivative. Please show steps!!! Thank you!!!
*Tuesday, February 25, 2014 at 7:18pm*

**Calculus**

DNE
*Tuesday, February 25, 2014 at 12:19am*

**Calculus**

the correct answer I was given has a negative 1/3 before the log. Also, how did you get the 1/3 value?
*Monday, February 24, 2014 at 8:47pm*

**Calculus**

we know that ∫cos(u) du = sin(u) ∫tan(u) du = -log cos(u) So, what we get here is (-1/3)sin(2-3x) - (-1/3)(-log cos(5-3x)) = -1/3 (sin(2-3x) + log cos(5-3x)) + C
*Monday, February 24, 2014 at 8:23pm*

**Calculus**

Evaluate the integral: (cos(2-3x) - tan(5-3x))dx
*Monday, February 24, 2014 at 7:23pm*

**Calculus - Derivatives**

If the original estimate was done by LEFT then the error is inversely proportional to the number of steps and the n = 30 error is (10/30) * -1.654 = -.551, approximately. So the estimate for n = 30 would be -.551 + 4.000 = 3.449 If the original estimate was done by TRAP then ...
*Monday, February 24, 2014 at 6:15pm*

**calculus**

check your graph against this one: http://www.wolframalpha.com/input/?i=tan%28x%29+for+5pi%2F3+%3C%3D+x+%3C%3D+3pi
*Monday, February 24, 2014 at 5:26pm*

**Calculus**

Just about every Calculus book I have ever seen uses this question as an introductory example of "rate of change" problem. At a time of t seconds, let the foot of the ladder be x ft from the wall, and the top of the ladder by y ft above the ground> then, x^2 + y^2...
*Monday, February 24, 2014 at 4:35pm*

**Calculus**

A ladder 25 feet long that was leaning against a vertical wall begins to slip. Its top slides down the wall while its bottom moves along the lever ground at a constant speed of 4 ft/sec. How fast is the top of the ladder moving when it is 20 feet above the ground?
*Monday, February 24, 2014 at 4:13pm*

**calculus**

5 pi/3 = 300 degrees 3 pi = 540 degrees so from -60 degrees around circle then to +180 degrees pick some points and do it be careful around 90 and 270 because tan is undefined along y axis
*Monday, February 24, 2014 at 3:19pm*

**calculus**

h(t)=tan theta (5pie/3,3pie) graph the function on the given interval
*Monday, February 24, 2014 at 3:12pm*

**calculus**

A simpler solution uses the fact that the area of an ellipse is πab Here, a=4 and b=5, so the area of the ellipse is 20π. Since all the triangles have the same height (6), the volume is (1/2)(6)(20π) = 60π
*Monday, February 24, 2014 at 1:29pm*

**calculus**

67
*Monday, February 24, 2014 at 5:53am*

**calculus**

for even values of n > 0 f has a min for odd values of n > 1, inflection
*Monday, February 24, 2014 at 5:03am*

**calculus**

Consider the function f(x)=x^n for positive integer values of n. (a) For what values of n does the function have a relative minimum at the origin? (b) For what values of n does the function have a point of inflection at the origin?
*Monday, February 24, 2014 at 2:27am*

**Math**

So in effect you are finding the vertex of the downwards opening parabola shortest way: the x of the vertex is -b/(2a) = -8/-.8 = 10 when x = 10 N(10) = -.4(100) + 8(10)+11 = 51 The ticket sales will peak at day 10 and on that day 51 tickets are sold method 2: complete the ...
*Sunday, February 23, 2014 at 9:45pm*

**calculus**

What about it ?
*Sunday, February 23, 2014 at 8:18pm*

**calculus**

h(t) = -1/3t^3 + 4t^2 + 20t +2, f or >- 2
*Sunday, February 23, 2014 at 7:13pm*

**calculus**

r = ln (x+2)/(x-1) (x+2)/(x-1) = e^r x+2 = e^r x - e^r x(2-e^r) = -e^r x = e^r/(e^r-2)
*Sunday, February 23, 2014 at 5:14pm*

**calculus**

k thanks soooo much!!!
*Sunday, February 23, 2014 at 3:53pm*

**calculus**

find dy/dx, the slope call it m at the given point use the point in the equation to find b in y = m x + b
*Sunday, February 23, 2014 at 3:26pm*

**calculus**

Exactly the same way I did the ellipse.
*Sunday, February 23, 2014 at 3:24pm*

**calculus**

not exactly sure how to solve it...... do i use the tangent line equation f(c+change in x)................???
*Sunday, February 23, 2014 at 3:05pm*

**calculus**

Now wait a minute. Try this one yourself first.
*Sunday, February 23, 2014 at 3:00pm*

**calculus**

Find the slope of the tangent line to the graph y = x-3 at the point (0.5, 8). Answer -48 -12 4 16
*Sunday, February 23, 2014 at 3:00pm*

**calculus**

8 y dy + 2 x dx = 0 so dy/dx = m = -x/4y at x = 3, y = -2 dy/dx = -3/(4y) = 3/8 = m so y = (3/8) x + b -2 = (3/8)3 + b b = -25/8 so y = (3/8) x -25/8 8 y - 3 x = -25 3 x - 8 y = 25 (b)
*Sunday, February 23, 2014 at 2:55pm*

**calculus**

2 x dx + x dy + y dx - 2 y dy = 0 dy ( x-2y) = - dx ( 2x + y) dy/dx = (2 x + y)/(2y-x) = slope at x = 2 4 + 2 y - y^2 = 5 y^2 - 2 y + 1 = 0 (y -1)^2 = 0 y = 1 so dy/dx = (5)/0 undefined
*Sunday, February 23, 2014 at 2:41pm*

**calculus**

Describe the slope of the tangent line to the curve defined by x 2 + xy - y 2 = 5 when x = 2. positive negative zero undefined
*Sunday, February 23, 2014 at 2:31pm*

**calculus**

Find the equation of the tangent line to the ellipse x 2 + 4y 2 = 25 when x = 3 and y < 0. Answer 3x - 8y = 7 3x - 8y = 25 3x + 8y = 7 3x + 8y = 25
*Sunday, February 23, 2014 at 2:25pm*

**calculus**

Solve for x: r(x)=ln (x+2/x-1)
*Sunday, February 23, 2014 at 1:04pm*

**calculus**

yes
*Sunday, February 23, 2014 at 9:01am*

**Pre-calculus**

your equation "falls apart" when p = 100 because you would be dividing by zero So mathematically, the cost would be infinitely large (that is, it is not possible) look at this graph and see what happens at p = 100 http://www.wolframalpha.com/input/?i=plot+C%...
*Saturday, February 22, 2014 at 12:07am*

**not Calculus Please help!**

B) compounded quarterly ----> i = .07/4 or .0175, and n = 6(4) or 24 amount = 7000(1.0175)^24 = $ 10,615.10 Do A and C the same way D amount = 7000 e^(6(.07)) = $ 10,653.73
*Friday, February 21, 2014 at 11:56pm*

**Calculus Please help!**

-8x + 4x dy/dx + 4y - 6y^2 dy/dx = 0 dy/dx(4x - 6y^2) = 8x - 4y dy/dx = (4x - 2y)/(2x - 3y^2) plug in x = 1 and y = 3 to find the slope
*Friday, February 21, 2014 at 11:53pm*

**Pre-calculus**

C=80,000p/(100-p) A)what happens of the company tries to remove 100 percent of the pollutants? Will it work or will it cost too much? B)draw a diagram to show what the consequences of the last question would be. Label the verticals asymptote(s) and analyze their impact on the ...
*Friday, February 21, 2014 at 11:39pm*

**Calculus Please help!**

If 7000 dollars is invested in a bank account at an interest rate of 7 per cent per year. A) Find the amount in the bank after 6 years if interest is compounded annually? B) Find the amount in the bank after 6 years if interest is compounded quaterly? C) Find the amount in the...
*Friday, February 21, 2014 at 11:29pm*

**Calculus Please help!**

Use implicit differentiation to find the slope of the tangent line to the curve at the point (1,3) -4x^2+4xy-2y^3=-46 m=____? ty guys so much!
*Friday, February 21, 2014 at 11:27pm*

**Calculus**

at least it looks like the last one :)
*Friday, February 21, 2014 at 1:42pm*

**Calculus**

Whoops, yes, use Steve's
*Friday, February 21, 2014 at 12:39pm*

**Calculus**

y = cx + x ln^2(x)
*Friday, February 21, 2014 at 12:35pm*

**Calculus**

That pesky y' gets in the way. The solution is really y = c1 e^x + c2 - 1/2 (sinx - cosx)
*Friday, February 21, 2014 at 12:33pm*

**Calculus**

x^3/(x+1)^2 = x - 2 + 3/(x+1) - 1/(x+1)^2 Now it's a piece of cake. ... Right?
*Friday, February 21, 2014 at 12:30pm*

**Calculus**

And you arrive there by using partial fractions: 1/(x^2-1)^2 = 1/4 (1/(x+1) + 1/(x+1)^2 - 1/(x-1) + 1/(x-1)^2)
*Friday, February 21, 2014 at 12:27pm*

**Calculus**

(1/4)[-2x/(x^2-1) - ln(1-x)+ln(1+x) ] + c used Wolfram alpha
*Friday, February 21, 2014 at 11:12am*

**Calculus**

¡ìdx/(x^2-1)^2
*Friday, February 21, 2014 at 10:30am*

**Calculus**

¡ì(up:1 down:0) (x^3 dx)/(x^2+2x+1)
*Friday, February 21, 2014 at 9:46am*

**Calculus**

probably sinusoidal y = a sin x + b cos x y' = a cos x - b sin x y" = -a sin x - b cos x = -y -a sx -b cx -a cx + b sx = 1 sx b = -a -a + b = 1 -2a = 1 a = -1/2 b = +1/2 so I get y = -(1/2) (sin x - cos x)
*Friday, February 21, 2014 at 8:27am*

**Calculus**

y"-y'=sin x solve in undetermined coefficients
*Friday, February 21, 2014 at 7:47am*

**Calculus**

Solve the differential equations
*Thursday, February 20, 2014 at 10:21pm*

**Calculus**

xy'-y=2xlnx
*Thursday, February 20, 2014 at 10:20pm*

**calculus - pi indeed**

Ah, yes. I forgot the √ in my integral. I also get 60π I thought it strange that there was no π, but I was in a hurry at the time. Score one more for Damon.
*Thursday, February 20, 2014 at 9:34pm*

**Calculus**

top and bottom both go to 0 try l'hopital derivative of top = 1(1)/(x+2)^2 --->1/4 derivative of bottom = 1 1/4 / 1 = 1/4
*Thursday, February 20, 2014 at 6:19pm*

**Calculus**

(-1/(x+2) + 1/2)/x = ((-2+x+2)/(2(x+2)))/x = (x/(2(x+2)))/x = 1/(2(x+2)) = 1/4 as x->0 No tricks here; just a little algebra
*Thursday, February 20, 2014 at 6:18pm*

**Calculus**

lim([-1/(x+2)]+1/2)/x as x->0
*Thursday, February 20, 2014 at 6:11pm*

**calculus**

Let's just do the quarter of it over the right half 0 < x < 5 and multiply by 2 at the end that means the triangle has base 2y and height 6 everywhere so its Area is (1/2)(2y)(6) = 6y and a slice of volume is 6ydx we need to integrate that from x = 0 to x = 5 (and ...
*Thursday, February 20, 2014 at 3:51pm*

**calculus**

using symmetry, we can see that since the area of each triangle is 1/2 yz v = 2∫[0,5] yz dx where y = 4√(1-x^2/25) and z=6 v = 48/5∫[0,5] ∫(25-x^2) dx = 800
*Thursday, February 20, 2014 at 3:30pm*

**calculus**

#3 A solid has a base in the form of the ellipse: x^2/25 + y^2/16 = 1. Find the volume if every cross section perpendicular to the x-axis is an isosceles triangle whose altitude is 6 inches. #4 Use the same base and cross sections as #3, but change the axis to the y-axis.
*Thursday, February 20, 2014 at 3:19pm*

**Math (pre calculus)**

As written, you have ax + b/cx + d = 2 acx^2 + (d-2)cx + b = 0 x = [c(2-d)±√((c(d-2))^2-4abc)]/2ac I assume you meant (ax+b)/(cx+d)=2 2(ax+b) = (cx+d) 2ax + 2b = cx + d (2a-c)x = d-2b x = (d-2b)/(2a-c)
*Thursday, February 20, 2014 at 1:49pm*

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